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Find the value of x. X-3 I 10

Find the value of x. X-3 I 10

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Last expert said it was 19.2, it's not.
## Problem 2 **Find the value of x.** **Diagram Explanation:** There is a circle divided into four regions by two perpendicular lines intersecting at the center. The lengths of three of the segments within those regions are provided: - One segment is labeled \( x - 3 \) - Another segment is labeled 10 - Another segment is labeled 18 - The final segment is labeled 9 **Answer Provided:** There is an answer entered that shows \( x = 10.2 \), which is marked incorrect. **Solution Approach:** To solve this problem, notice that the given segments create two pairs of opposite segments. The sum of each pair of opposite segments must be equal because they both span the same diameter of the circle. - For the pair involving \( x - 3 \) and 18: \[ (x - 3) + 18 \] - For the pair involving 10 and 9: \[ 10 + 9 = 19 \] Set these sums equal to each other: \[ x - 3 + 18 = 19 \] Simplify the equation: \[ x + 15 = 19 \] Solving for \( x \): \[ x = 19 - 15 \] \[ x = 4 \] Therefore, the correct value of \( x \) is 4. Make sure to re-check calculations as the value \( x = 10.2 \) previously entered was incorrect.
Transcribed Image Text:## Problem 2 **Find the value of x.** **Diagram Explanation:** There is a circle divided into four regions by two perpendicular lines intersecting at the center. The lengths of three of the segments within those regions are provided: - One segment is labeled \( x - 3 \) - Another segment is labeled 10 - Another segment is labeled 18 - The final segment is labeled 9 **Answer Provided:** There is an answer entered that shows \( x = 10.2 \), which is marked incorrect. **Solution Approach:** To solve this problem, notice that the given segments create two pairs of opposite segments. The sum of each pair of opposite segments must be equal because they both span the same diameter of the circle. - For the pair involving \( x - 3 \) and 18: \[ (x - 3) + 18 \] - For the pair involving 10 and 9: \[ 10 + 9 = 19 \] Set these sums equal to each other: \[ x - 3 + 18 = 19 \] Simplify the equation: \[ x + 15 = 19 \] Solving for \( x \): \[ x = 19 - 15 \] \[ x = 4 \] Therefore, the correct value of \( x \) is 4. Make sure to re-check calculations as the value \( x = 10.2 \) previously entered was incorrect.
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